Evaluating Functions
Evaluating Functions
To evaluate a function is to:
Replace (substitute) any variable with its given number or expression
Like in this example:
Example: evaluate the function f(x) = 2x+4 for x=5
Just replace the variable "x" with "5":
f(5) = 2×5 + 4 = 14
Answer: f(5) = 14
More Examples
Here is a function:
f(x) = 1 − x + x2
f is just a name,
x is just a place-holder.
These are all the same function:
- f(x) = 1 − x + x2
- f(q) = 1 − q + q2
- w(A) = 1 − A + A2
- pumpkin(θ) = 1 − θ + θ2
Evaluate For a Given Value:
Let us evaluate that function for x=3:
f(3) = 1 − 3 + 32 = 1 − 3 + 9 = 7
Evaluate For a Given Expression:
Evaluating can also mean replacing with an expression (such as 3m+1 or v2).
Let us evaluate our function for x=1/r:
f(1/r) = 1 − (1/r) + (1/r)2
Or for x=a−4:
Another Example
You can use your ability to evaluate functions in other way:
Example: h(x) = 3x2 + ax − 1
- You are told that h(3) = 8, can you work out what "a" is?
Check:
h(3) = 3(3)2 − 6×3 − 1 = 27 − 18 − 1 = 8 
Careful!
I recommend putting the substituted values inside parentheses () , so you don't make mistakes.
Example: evaluate the function h(x) = x2 + 2 for x = −3
Replace the variable "x" with "−3":
h(−3) = (−3)2 + 2 = 9 + 2 = 11
Without the () you could make a mistake:
h(−3) = −32 + 2 = −9 + 2 = −7 (WRONG!)
Also be careful of this:
f(x+a) is not the same as f(x) + f(a)
Example: g(x) = x2
vs
Different Result!